How do you find the equation?

Answer:

Step-by-step explanation:

1.To arrange all 6 tables in a line, we can use the factorial function which calculates the product of all positive integers up to a given number. We can write:

6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

Therefore, there are 720 ways to arrange all 6 tables in a line.

2.To choose 4 out of the 6 tables, we can use the combination function, which calculates the number of ways to choose k items out of n distinct items, without regard to their order. We can write:

C(6,4) = 6! / (4! x 2!) = (6 x 5 x 4 x 3) / (4 x 3 x 2 x 1) = 15

Therefore, there are 15 ways to choose 4 out of the 6 tables.

There are 720 ways to arrange all 6 tables in a line.

And, there are 15 ways to choose 4 out of the 6 tables.

A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Given that;

Mrs. Smith has 6 activity tables she wants to line up side by side in her classroom.

Now, After arrange all 6 tables in a line, we can use the factorial function which calculates the product of all positive integers up to a given number. We can write:

6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

Hence, there are 720 ways to arrange all 6 tables in a line.

And, For choose 4 out of the 6 tables, we can use the combination function, which calculates the number of ways to choose k items out of n distinct items, without regard to their order. We can write:

⁶C₄ = 6! / (4! x 2!)

= (6 x 5 x 4 x 3) / (4 x 3 x 2 x 1)

= 15

Thus, there are 15 ways to choose 4 out of the 6 tables.

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Answer:

The area of the shaded sector is

(π/4)(6^2) = (π/4)(36) = 9π

Step-by-step explanation:

The value of the expression can be calculated using the order of operations, also known as PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

The expression is:

2 + [(15 + 3) × 2]

According to PEMDAS, we should first evaluate the expression within the parentheses:

15 + 3 = 18

So, the expression becomes:

2 + [18 × 2]

Next, we perform the multiplication:

18 × 2 = 36

Now, we substitute the result back into the original expression:

2 + 36

Finally, we perform the addition:

2 + 36 = 38

So, the value of the given expression is 38.

Therefore , the solution of the given problem of ratio comes out to be this indicates that there are 4 black pens in the package for every red pen.

A group comprising values both variable "a" and "" that seem to be equal is found using the straightforward formula "a / b," whenever "b" might be a greater number than zero. A ratio is created by combining two ratios. The ratio , fraction could have been 1:1 if there were just one guy and three women. There are 1/4 men and 3/4 women in the group.

Here,

By dividing the numerator and denominator by their greatest common divisor (GCD), the ratio 3/12 can be made simpler.

Due to the fact that both 3 and 12 can be divided by 3, their GCD equals 3.

The result of dividing the numerator and denominator by 3 is:

=> 3 ÷3 = 1.

=> 12 ÷ 3 = 4

Thus, 1/4 is the simple ratio that corresponds to 3/12.

Let's now use a simplified equivalent ratio to represent the ratio of red to black pens in the package:

Black pens 3: 12 Red pens:

=> 3 ÷ 3 = 1

=> 12 ÷ 3 = 4

Consequently, the rounded equivalent ratio of red to black pens is 1 to 4.

This indicates that there are 4 black pens in the package for every red pen.

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Answer: The correct answer is 8.12%-11.88%.

We can use the formula for a confidence interval for a proportion:

p ± z*SE

where p is the sample proportion, z* is the z-score corresponding to the desired level of confidence (in this case, 1.96 for a 95% confidence interval), and SE is the standard error of the proportion.

SE = sqrt(p*(1-p)/n) = sqrt(0.1*0.9/1015) = 0.0094

Plugging in the values, we get:

0.1 ± 1.96*0.0094

= 0.1 ± 0.0184

So the 95% confidence interval is (0.0816, 0.1184), which is equivalent to 8.12%-11.88%.

Step-by-step explanation:

The slant height of the Teepee is 32.76 feet.

The square footage of one of the rooms is 44 square feet.

Check the attached for the sketch of the cone. From the image, the slant height is labelled l. Note that the base diameter is 14 feet, so the base radius will be 7 feet.

(a) Thus, the slant height can be found by considering one of the right triangles in the cone. That is:

l² = 32² + 7²   (Pythagoras Theorem)

l²  = 1024 + 49

l = √1073

l = 32.76 feet

(b) The shape of base is a circle.

Area of circle = πd

where d is the base diameter

Area of circle = 22/7 * 14

Area of circle = 44 square feet

Thus, the square footage of one of the rooms is 44 square feet

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The journal entries fro the transaction for October 31 and November 19 are as follows:

Oct. 31: Cash                                              $3,840,000

             ($12 x 320,000)

                       Common Stock                                      $1,600,000

                       ($5 x 320,000)

                       Paid-In Capital in Excess of Par-com.   $2,240,000  

                       ($3,840,000 - $1,600,000)

Nov. 19: Cash                                            $3,240,000

              ($72 x 45,000)

                       Preferred Stock                                     $2,700,000

                        ($60 x 45,000)

                       Paid-In Capital in Excess of Par-Pre.    $540,000

                        ($3,240,000 - $2,700,000)

Full question "On October 31, Pidgeon Stones Inc. , a marble contractor, issued for cash 320,000 shares of $5 par common stock at $12, and on November 19, it issued for cash 45,000 shares of preferred stock, $60 par at $72. Journalize the entries for October 31 and November 19".

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From shortest to longest is:  C. Marisol, Juan, Lucia, Jamal.

By comparing the lengths of the students' walks, it is possible to determine the correct order of the students based on their walks.

Marisol walks 0.62 miles, while Juan walks one mile. So Juan's walk isn't the most limited.

Lucia walks one mile, which is shorter than Jamal's walk of 0.78 miles but longer than Marisol's walk of 0.62 miles. Therefore, neither the shortest nor longest walk is Lucia's.

Therefore, Jamal and Marisol remain choices. The correct order, from shortest to longest, is as follows because Jamal's walk is longer than Marisol's:

C. Marisol, Juan, Lucia, Jamal.

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Using relevant theorems the measures are:

1. x = 61°; y = 61°    2. x = 12; y = 7   3. x = 5; y = 13

4. x = 97°;    5. x = 6  6. x = 9

1. x = 61° [based on the vertical angles theorem]

y = 61° [based on the corresponding angles theorem]

2. 8x = 96 [based on the corresponding angles theorem]

x = 96/8

x = 12

8x = 11y + 19 [based on the vertical angles theorem]

Plug in the value of x:

8(12) = 11y + 19

96 = 11y + 19

96 - 19 = 11y

77 = 11y

77/11 = y

y = 7

3. 8x + 2 = 42 [based on the alternate interior angles theorem]

8x = 42 - 2

8x = 40

x = 40/8

x = 5

8x + 2 + [6(2y - 3)] = 180 [based on the linear angles theorem]

8(5) + 2 + 12y - 18 = 180

40 + 12y - 16 = 180

24 + 12y = 180

12y = 180 - 24

12y = 156

y = 156/12

y = 13

4. x = 97° [corresponding angles theorem]

5. 8x = 4x + 24 [based on the alternate exterior angles theorem]

8x - 4x = 24

4x = 24

x = 6

6. 11x + 33 + 6x - 6 = 180

17x + 27 = 180

17x = 180 - 27

17x = 153

x = 9

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Answer:

-5

Step-by-step explanation:

if u graph it, you can see where the y-intercept is.

To find the 18th term of a pattern that repeats 5 times (which is a pentagon), we need to divide 18 by 5, which gives us a quotient of 3 and a remainder of 3.

This means that the pattern repeats 3 times, and we need to find the 3rd term of the pattern after the third pentagon.

The third term of the pattern after the third pentagon would be the fourth pentagon in the sequence, since each pentagon consists of 5 terms. Therefore, the 18th term would be the third term of the fourth pentagon in the sequence, which is the 13th term overall.

So the 18th term in the sequence would be the 13th term of the pattern, which is another pentagon.

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The final expression that gives us the cost of x skirts and y hats in pounds is 24x + 15y.

In this case, our variables are x and y, which represent the number of skirts and hats, respectively. Our constants are 24 and 15, which represent the cost of one skirt and one hat, respectively. And our operations are multiplication and addition.

The cost of x skirts is simply the cost of one skirt (which is 24) multiplied by the number of skirts (which is x). So, the expression for the cost of x skirts would be:

24x

Similarly, the cost of y hats is the cost of one hat (which is 15) multiplied by the number of hats (which is y). So, the expression for the cost of y hats would be:

15y

To find the total cost of x skirts and y hats, we simply add the two expressions together. Thus, the expression for the cost in pounds of x skirts and y hats is:

24x + 15y

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Answer:

100ft²

Step-by-step explanation:

to find the area of the figure you must do the area of the small rectangle plus the area of the large rectangle

area = length* width

so the area of the small rectangle equals

7ft * 4ft = 28ft²

then the large rectangle

9ft*8ft=72ft²

28ft²+72ft²=100ft²

None of the provided circle graphs correctly represents the data in the table.

The total number of visitors in the table is 300, but the percentages in all the circle graphs add up to more than 100%, indicating that the data has been incorrectly represented.

To create a correct circle graph, we need to calculate the percentage of visitors for each type of transportation, which can be done by dividing the number of visitors for each type by the total number of visitors (300) and multiplying by 100.

Walk: (120/300) x 100 = 40%

Bicycle: (24/300) x 100 = 8%

Car Service: (45/300) x 100 = 15%

Bus: (30/300) x 100 = 10%

Subway: (81/300) x 100 = 27%

Thus, a correct circle graph representing the data in the table would have five sections labeled "Walk 40%", "Bicycle 8%", "Car Service 15%", "Bus 10%", and "Subway 27%".

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The completed checking account register can be presented as follows;

[tex]\begin{tabular}{ | c | c | l | c | c | c |}\cline{1- 6}Date & Check \# & Transaction Description & Payment (-) & Deposit (+) & Balance \\cline{1-6}\cline{1- 6}06/30 & --- & Beginning Balance & - & \$150 & \$150 \\cline{1- 6}\cline{1- 6}07/01 & 0001 & Rent payment & \$500.00 & - & \$-350 \\cline{1-6}\cline{1- 6}07/01 & --- & Paycheck & --- & \$575 & \$225 \\cline{1-6}\cline{1- 6}07/07 & 0002 & Utilities & \$102.74 & --- & \$122.26 \\cline{1-6}\cline{1- 6}\cline{1- 6}\end{tabular}[/tex]

[tex]\begin{tabular}{ | c | c | l | c | c | c |} \cline{1- 6} \cline{1- 6} Date & Check \# & Transaction Description & Payment (-) & Deposit (+) & Balance \ \cline{1-6} \cline{1- 6} 07/08 & --- & Groceries & \$64.96 & - & \$57.30 \ \cline{1-6} \cline{1- 6} \cline{1-6}07/10 & --- & Babysitting & - & \$42.00 & \$99.30 \ \cline{1-6} \cline{1-6} \cline{1- 6} 07/12 & --- & Movies & \$18.65 & - & \$80.65\ \cline{1-6} \cline{1- 6} 07/14 & --- & Gas & \$31.61 & - & \$49.04 \ \cline{1- 6} \cline{1- 6} \end{tabular}[/tex]

[tex]\begin{tabular}{ | c | c | l | c | c | c |}\cline{1- 6}Date & Check \# & Transaction Description & Payment (-) & Deposit (+) & Balance \ \\\cline{1-6} 07/15 & --- & Paycheck & - & \$575 & \$624.04 \ \cline{1-6} \cline{1-6} 07/19& 0003&Car Insurance&\$78.50&-&\$545.54\cline{1-6} \cline{1-6} 07/22&---&Groceries&\$58.30&-&\$487.24\cline{1-6} \cline{1-6} \end{tabular}[/tex]

[tex]\begin{tabular}{ | c | c | l | c | c | c |}\cline{1-6}Date & Check # & Transaction Description & Payment (-) & Deposit (+) & Balance \ \cline{1-6} \cline{1-6} 07/26&0004&Phone&\$80&-&\$407.24 \cline{1-6}\cline{1-6}07/26 & 0005 & Internet & \$62.75 & - & \$344.49 \ \cline{1-6}\cline{1-6}07/28 & 0006 & Cable TV& \$87.00 & - & \$257.49 \ \cline{1-6}\cline{1-6}07/30 & --- & Gas & \$35.22 & - & \$222.27 \ \cline{1-6}\cline{1-6}\end{tabular}[/tex]

A check register, which may also be known as a cash disbursement journal is a register for recording the transactions done with check and cash, by a business during an accounting period.

Some of the reasons why it is important to examine bank records includes;

1. To ensure accuracy; When bank records are regularly checked, it ensures that transactions using a bank account are recorded accurately

2. To prevent fraud; Bank record review help prevents fraud which includes identity theft, charges which are not authorized, and other forms of fraudulent activity

3. Budget planning and monitoring; Bank record examination ensures visualization of where money in a bank account is going, such as to enable proper planning, and budgeting

4. Resolution of disputes; Disputes such as unauthorized credit or debit on an account can be detected and raised with a bank when a bank account is checked regularly.

5. Maintaining good financial health; Regular examination of bank records help ensures that a bank account is secure and accurate.

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We can start by drawing a diagram of the situation:

The width of the path is 24 meters.

Let's call the width of the path "x".

The dimensions of the inner rectangle (the lawn without the path) are 46m by 34m. The dimensions of the outer rectangle (the lawn with the path) are (46+2x) by (34+2x).

Area of path = Area of outer rectangle - Area of inner rectangle

425m² = (46+2x)(34+2x) - (46)(34)

Simplifying and solving for x:

425m² = (2x+46)(2x+34)

425m² = 4x² + 80x + 1564

4x² + 80x - 1161 = 0

We only want the positive value for x, so:

x = (-80 + 272) / 8

x = 24m

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Using mathematical operations of division and multiplication, the total weight of the order in pounds is 3 pounds.

The total weight is firstly computed in ounces before being converted into pounds.

The computation follows the mathematical operations of multiplication and division, respectively.

The number of Orange You Fresh soap bars ordered by a customer = 12

The weight of each bar of soap = 4 ounces

The total weight of 12 bars in ounces = 48 ounces (4 x 12)

1 pound = 16 ounces

3 pounds = 48 ounces (48 ÷ 16)

Thus, based on mathematical operations, the number of pounds this order will weigh is 3 pounds.

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Answer:

240m

Step-by-step explanation:

You need to find the area of each surface.

FORMULAS

A= L × W

A= 1/2(L × W)

SIDES

Base = 12×6 = 72

Top of triangle = 6×13 = 78

Side of triangle = 5×6 = 30

Triangular side 1 = 1/2(5×12) = 30

Triangular side 2 = 1/2(5×12) 30

Now you need to add all of the surface areas together.

72+78+30+30+30 = 240

Therefore, the surface area of the triangular prism is 240m.

IM SO SORRY IF THIS DOESN'T MAKE ANY SENSE!

Answer:

x = 8/3

Step-by-step explanation:

y = mx + b

y = -3x + 16

8 = -3x + 16

Subtract 16 from both sides

-8 = -3x

Divide both sides by -3

8/3 = x

The value of | a b c 7d + a 7e + b 7f + c g h i| is given by -35 + b(ch - di) + c(gi - eh) + a(hk - fg).

Expanding the determinant using the first row, we get:

| a b c 7d + a 7e + b 7f + c g h i|

= a | b c 7d + 7e b 7f + g h i| - b |a c 7d + 7e c 7f + g h i| + c |a b 7d + 7e 7f + g h i|

= a | b c 7d + 7e b 7f + g h i| + b |a c 7d + 7e c 7f + g h i| - c |a b 7d + 7e 7f + g h i|

Now, we can expand each of the three determinants on the right-hand side using the first row and simplify:

| b c 7d + 7e b 7f + g h i| = b | c 7f h i| - 7e |b 7f h i| + g |b c h i|

= -7e b |7f h i| + g |b c h i| - h |b c 7f i| + i |b c 7f h|

= -7e bi + gh - bhf + chi

|a c 7d + 7e c 7f + g h i| = a |c 7f h i| - 7e |c 7d h i| + g |c 7d 7f i|

= 7e ac - gci + chd - ahf

|a b 7d + 7e 7f + g h i| = a |b 7f h i| - 7e |b 7d h i| + g |b 7d 7f i|

= -7e ab + ghi - bgd + aef

Substituting these expressions back into the expanded determinant and simplifying, we get:

| a b c 7d + a 7e + b 7f + c g h i|

= a(-7e bi + gh - bhf + chi) + b(7e ac - gci + chd - ahf) + c(-7e ab + ghi - bgd + aef)

= -7abe - 7bdf - 7cfg + 7aef + bch + cgi + ahk - ceh - afg - bdi

= -7(abe + bdf + cfg - aef) + (bch + cgi + ahk - ceh - afg - bdi)

Since |a b c d e f g h i| = 5, we have:

abe + bdf + cfg - aef = 5

Therefore, we can simplify the expression further:

| a b c 7d + a 7e + b 7f + c g h i|

= -7(5) + (bch + cgi + ahk - ceh - afg - bdi)

= -35 + b(ch - di) + c(gi - eh) + a(hk - fg)

Hence, the value of | a b c 7d + a 7e + b 7f + c g h i| is given by -35 + b(ch - di) + c(gi - eh) + a(hk - fg).

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The simplified expression for | a b c 7d + a 7e + b 7f + c g h i| is 7| a b c d g h i| + 7| a b c e g h i| - 35.

First, factor out the 7 from the second row:

| a b c 7(d + e + f) g h i| = 7| a b c d + e + f g h i|

Expand the second row using the property of determinants that allows us to break up a row sum:

7(| a b c d g h i| + | a b c e g h i| + | a b c f g h i|)

Now, use the property of determinants that allows us to switch rows and multiply by -1:

7(| a b c d g h i| + | a b c e g h i| - | d e f a b c g h i|)

Recognize that the third determinant is equivalent to the given determinant, but with rows 1 and 3 switched, which

gives us:

7(| a b c d g h i| + | a b c e g h i| - 5)

Finally, multiply 7 by the expression inside the parentheses:

7| a b c d g h i| + 7| a b c e g h i| - 35

So, the simplified expression for | a b c 7d + a 7e + b 7f + c g h i| is 7| a b c d g h i| + 7| a b c e g h i| - 35.

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The equation that can be used to represent number of people who can go to the amusement park is 12 + 33.75x = 215.50.

We have,

the total amount to spent on amusement park = $214.50

And the parking fees = $12

The ticket cost per person = $33.75

let the number of person be x.

Then, the equation can become as

12 + 33.75x = 215.50

Simplifying the equation we get

33.75x = 215.5 - 12

33.75x = 203.5

x= 6.02

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The equation used to determine the number of days, x, required for the substance to decay to 63 grams is: x ≈ 83.60

To determine the number of days, x, required for a radioactive substance to decay to 63 grams, we can use the exponential decay formula. The equation that represents the decay of a radioactive substance over time is:

N(t) = N₀ * (1/2)^(t/h)

Where:

N(t) is the remaining mass of the substance at time t

N₀ is the initial mass of the substance

t is the time elapsed

h is the half-life of the substance

In this case, we have an initial mass of 475 grams, and we want to find the number of days required for the substance to decay to 63 grams. We can set up the equation as follows:

63 = 475 * (1/2)^(x/20)

To solve for x, we can isolate the exponential term on one side of the equation:

(1/2)^(x/20) = 63/475

Next, we can take the logarithm (base 1/2) of both sides to eliminate the exponential term:

log(base 1/2) [(1/2)^(x/20)] = log(base 1/2) (63/475)

By applying the logarithmic property log(base b) (b^x) = x, the equation simplifies to:

x/20 = log(base 1/2) (63/475)

Finally, we can solve for x by multiplying both sides of the equation by 20:

x = 20 * log(base 1/2) (63/475)

Using a calculator to evaluate log(base 1/2) (63/475) ≈ 4.1802, we find:

x ≈ 20 * 4.1802

x ≈ 83.60

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The domain of the expression is all real numbers except -7 and 5. In interval notation, the domain can be expressed as (-∞, -7) U (-7, 5) U (5, ∞).

The simplified form of the expression is:

(12 - X) / (x² + 2x - 35) * (x² + 7x) / (x² - 12x)

And the domain of the expression is all real numbers except for values of x that make the denominators equal to zero, as division by zero is undefined.

To find the values of x that make the denominators equal to zero, we can set the denominators equal to zero and solve for x:

x² + 2x - 35 = 0

(x + 7)(x - 5) = 0

x + 7 = 0 or x - 5 = 0

x = -7 or x = 5

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The function best models the data in the table is y=-0.6x+132 (option a).

The table shows the minimum target heart rates by age, which implies that as a person ages, their heart rate should be maintained within a certain range during exercise to achieve optimal cardiovascular benefits. In order to determine the target heart rate for a given age, we need a mathematical function that can accurately model the data in the table.

This is a linear function, which means that it assumes a constant rate of change in the target heart rate as age increases.

However, the data in the table shows that the target heart rate decreases gradually with age. Therefore, this function does  accurately model the data and is a suitable option.

Hence (a) is the right one.

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Complete Question:

Age x (year)                           Minimum Target Heart Rates by Age

30                                                                114

35                                                                 111

40                                                                108

45                                                                105

50                                                                102

Which function best models the data in the table?

a) y=-0.6x+132

b) y=(x-30)²+114

c) y= 19/30x

We need to round up to the nearest integer, the required sample size is 76 households.

To estimate the required sample size, we can use the formula:

[tex]n = (z^2 * s^2) / E^2[/tex]

Where:

z is the z-score corresponding to the confidence level (90% = 1.645)

s is the standard deviation of the population (square root of the variance, so s = sqrt(3.61) = 1.898)

E is the maximum error allowed (0.15 gallons)

Plugging in the values, we get:

[tex]n = (1.645^2 * 1.898^2) / 0.15^2[/tex]

n = 75.57

Since we need to round up to the nearest integer, the required sample size is 76 households.

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As per the concept of simple interest, the interest amount earned after three years is $306.

To calculate the interest amount earned, we can use the formula:

I = P * r * t

Where:

I = interest earned

P = principal amount

r = interest rate per year (as a decimal)

t = time period in years

Plugging in the values from the problem, we get:

I = $1200 * 0.085 * 3

I = $306

This means that after three years, the bond will be worth the principal amount plus the interest earned, which is:

$1200 + $306 = $1506

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Answer:

4

Step-by-step explanation:

4-0=4

Answer:

4 left

Step-by-step explanation:

then you have 4 apples

A reduced echelon matrix in R3 is 1--1 if and only if the homogeneous system Ax = 0 has only the trivial solution if and only if there are no free variables.

The statement is true.

A reduced echelon matrix in R3 represents a linear system of equations that can be solved using Gaussian elimination.

The reduced echelon form of a matrix is obtained by performing row operations that reduce the matrix to a triangular form, with ones on the main diagonal and zeros below it.
If the homogeneous system Ax = 0 has only the trivial solution, it means that the only solution to the system is the zero vector.

In other words, there are no non-zero vectors that satisfy the system.

This is equivalent to saying that the rank of the matrix is equal to the number of columns, or in other words, there are no free variables in the system.
If the system has no free variables, it means that each variable can be expressed as a unique function of the other variables.

This implies that the system has a unique solution, or in other words, the mapping from the system of equations to the solution vector is one-to-one.
If the system is one-to-one, it means that each solution vector corresponds to a unique system of equations.

This implies that there are no redundant equations or variables, and therefore no free variables.

Hence, the homogeneous system Ax = 0 has only the trivial solution.
The statement is true.

A reduced echelon matrix in R3 is 1--1 if and only if the homogeneous system Ax = 0 has only the trivial solution if and only if there are no free variables.

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Answer:

ight, whats good.

To calculate the percentage of students who brought lunch from home, we can use the following formula:

Percentage = (Number of students who brought lunch from home / Total number of students) * 100

Given:

Number of students who ate school lunch = 114

Number of students who brought lunch from home = 266

Total number of students = Number of students who ate school lunch + Number of students who brought lunch from home = 114 + 266 = 380

Plugging in these values into the formula:

Percentage = (266 / 380) * 100 = 70%

So, 70% of the students brought lunch from home.